Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #11757174 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting, socle | C24×C5 ⋊ Dic3 |
| derived | C5×C22⋊A4 ⋊ C4 |
| Sylow | C5 ⋊ #5936 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C5×C22⋊A4 | C4 |
| Fitting, socle | C24×C5 | Dic3 |
| prime radical, cosocle | D5×C22⋊A4 | C2 |
| LCS | G ▷ C5×C22⋊A4 | |
| UCS | C1 | |
300 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^2,3,5,2^4|a^2=b,c^a=c^2,d^a=d^3,e^a=f,f^a=e,g^a=h,h^a=g,d^b=d^4,e^c=f,f^c=ef,g^c=gh,h^c=g28 conjugacy classes — view the full character table.
| maximal subgroup of | #1020⋊AGL(1,𝔽5), #14512453, AGL(1,𝔽5)×#1020, … |
| maximal normal subgroup of | #1020⋊AGL(1,𝔽5), #14512453, AGL(1,𝔽5)×#1020, … |
| maximal quotient of | #14514390, #14514391, #14514392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11369);